CN106485269A - SAR image object detection method based on mixing statistical distribution and multi-part model - Google Patents

Abstract

The present invention provides a kind of SAR image object detection method based on mixing statistical distribution and multi-part model, first SAR image training set is carried out mixing statistical distribution modeling, build spatial pyramid including to SAR image all in training set respectively, then any layer subimage in pyramid is set up with mixing statistical distribution pattern, the expression formula of mixing statistical distribution pattern is taken the logarithm, then expectation-maximization algorithm is combined with MoLC method for parameter estimation, the parameter of mixing statistical model is estimated；Multi-part model training and target detection, mixing statistical distribution is combined with multi-part model, to all picture construction mixing Statistical Distribution Characteristics pyramids in SAR image training set, according to root filtering window and part filtering window, obtains target detection frame.Present invention mixing Statistical Distribution Characteristics are combined with the structural information of multi-part model, are capable of the overall accurate detection with structure of different target in SAR image.

Description

SAR image target detection method based on mixed statistical distribution and multi-component model

Technical Field

The invention belongs to the technical field of image processing, and particularly relates to an SAR image target detection method based on mixed statistical distribution and a multi-component model.

Background

Since the speckle noise in the SAR image can be regarded as the fluctuation of the observed value on the average characteristic, the speckle noise is statistically modeled, and the sensor and the surface information in the speckle noise can be effectively utilized. The statistical distribution model of the SAR image is divided into a parametric model and a non-parametric model. The construction process of the parametric model is to assume that actual SAR image data obey different probability distributions respectively, and determine the probability distribution of the optimal fitting SAR data distribution according to an evaluation criterion through parameter estimation. The non-parametric model is constructed by adopting different kernel functions to perform weighted summation to realize the modeling of image data distribution, such as methods of a support vector machine, a neural network, a Parzen window and the like. The modeling method is more flexible, has higher estimation precision, is suitable for estimating more complex image probability distribution, but needs a large amount of sample data for training, and has lower efficiency. In contrast, therefore, parametric models are more widely studied and applied.

Parametric models are classified into four categories according to different sensor parameters and scattering mechanisms of different surface feature targets: empirical distribution models, statistical distributions based on product models, statistical distributions based on the generalized central limit theorem, and other distribution models. The empirical distributions are derived primarily from actual data analysis experience, including log-normal distributions and Weibull distributions. A statistical model based on a product model is established on the basis of a coherent speckle model, and the measured value of the SAR image is obtained by subjecting a radar scattering cross section of a ground object to multiplicative speckle noise, wherein the measured value comprises Rayleigh distribution, K distribution and the like. The statistical distribution model based on the generalized central limit theorem considers that under the condition that the variance of a group of independent same-distribution random variables is limited or infinite, the sum of the independent same-distribution random variables is converged to alpha-stable distribution, and the statistical model comprises the alpha-stable distribution and symmetrical alpha steady-state (S alpha S) distribution. Other distribution models include Racian distribution, joint distribution models, Gaussian mixture distribution, and the like.

In SAR image target detection based on statistical distribution, the statistical distribution is usually combined with the CFAR method. The CFAR method is a method of adaptively acquiring a detection threshold under a constant false alarm rate condition according to the statistical characteristics of the SAR image. If the fitting accuracy of the statistical distribution model to the SAR image data is poor, the performance of the corresponding CFAR method is greatly influenced, and the requirement of target detection cannot be met. In addition, basically, all CFAR methods based on statistical distribution select a target detection threshold according to the difference between the background of the SAR image and the statistical information of the target distribution, but this method does not consider the statistical distribution characteristics of the target, but detects the target as an abnormal point in the background area, so this method is a suboptimal statistical detection method.

At present, due to the importance of many countries in the world and the investment of a large amount of manpower and material resources, the research and development work of the high-resolution SAR sensor is greatly advanced. The high-resolution SAR image provides richer target information and category information, so that whether a target exists can be judged, and the shape, the state and the information of each component of the target can be learned, and higher requirements are provided for a target detection technology.

Disclosure of Invention

The invention aims to provide a novel SAR image target detection method based on mixed statistical distribution and a multi-component model aiming at the problem of high-resolution SAR image target detection.

The technical scheme of the invention is that an SAR image target detection method based on mixed statistical distribution and a multi-component model comprises the following steps:

step 1, carrying out mixed statistical distribution modeling on an SAR image training set, wherein the mixed statistical distribution modeling comprises the following substeps;

step 1.1, respectively constructing a spatial pyramid for all SAR images in a training set, and then establishing a mixed statistical distribution model for any layer of subimages in the pyramid;

step 1.2, taking logarithm of an expression of the mixed statistical distribution model, and then combining an expectation maximization algorithm with a MoLC parameter estimation method to estimate parameters of the mixed statistical model;

step 2, training a multi-component model and detecting a target, wherein the multi-component model training and target detection method comprises the following substeps;

step 2.1, according to the parameter estimation result obtained in the step 1, combining the mixed statistical distribution with a multi-component model, firstly determining the initial value and the position of a root filter and the initial value and the position of a component filter on an SAR image training set by a standard SVM method, then obtaining the fractions of the root filter and the component filter by introducing an expansion factor based on the target length-width ratio, and finally updating the root filter and the component filter by adopting a Latent SVM method;

and 2.2, constructing a mixed statistical distribution characteristic pyramid for all images in the SAR image training set, searching on each layer of the characteristic pyramid in a rectangular sliding window mode, sequentially recording the coordinates and the scores of the positions of the optimal root filters, the part filter labels and the part filter coordinates, and keeping the root filter window and the part filter window as a target detection frame when the comprehensive scores in the detection window are larger than a detection threshold value.

Moreover, the implementation manner of establishing the mixed statistical distribution model for any layer of the sub-images of the pyramid in the step 1.1 is as follows,

let X be { X ═ X₁,...,x_nDenotes any layerNeighborhood sub-block, x, of image sample point₁,…,x_nThe pixel points in the subblocks are referred to, n refers to the number of the pixel points in the subblocks, the probability density function F (X) of the neighborhood subblocks is expressed as the linear weighting of K statistical distributions,

wherein p is_i(θ_i) Representing the ith probability density distribution, θ, in the mixture distribution_iRepresenting a model parameter representing the ith probability density distribution, w_iA weight representing the ith probability density distribution,and w is not less than 0_iLess than or equal to 1, and K represents the number of the mixed statistical distribution models;

the parameter vector to be estimated for each sample point is Θ ═ w₁,w₂,...,w_K；θ₁,θ₂,...,θ_KAnd the mixed distribution model of any layer of sub-images is expressed as,

wherein N refers to the number of neighborhood sub-blocks, X_jRefers to the jth neighborhood sub-block.

Moreover, in step 1.2, the expectation-maximization algorithm is combined with the MoLC parameter estimation method, and the parameters of the mixed statistical model are estimated in the following manner,

(a) step E, let t represent iteration times, posterior probability based on current parameterAs indicated by the general representation of the,

wherein,andrespectively representing the ith probability density distribution and probability weight after t iterations,representing the corresponding distribution parameters;

(b) m, adopting MoLC parameter estimation, obtaining the weight of the ith probability density distribution by a histogram-based estimation method, expressing the weight as the formula,

wherein,representing a set of sample points, y, subject to an ith probability density distribution^t(x) { -1,1} represents the label of the sample point x after t iterations, 1 represents the target, -1 represents the background, h (x) represents the histogram;

updating the distribution parameter θ according to the MoLC equation^t+1The estimation method of the MoLC equation is expressed as,

wherein,representing a logarithmic moment;

the parameter updating is realized by adopting an EM iteration mode, initializing a parameter theta based on the MoLC, and then taking a label value when the posterior probability is maximum as the final class of the image in the iteration process;

the above process is repeated until a convergence state is reached.

Furthermore, the implementation of said step 2.1 is as follows,

combining the mixed statistical distribution with the multi-component model, wherein distribution parameters obtained by the statistical distribution are used as the characteristic description of the target in the component model, and the corresponding parameters comprise mixed statistical distribution model parameters theta { w ═ w }₁,w₂,...,w_K；θ₁,θ₂,...,θ_KAnd component model position information parameter P_m＝(F_m,υ_m,s_m,d_m) Hidden variable z ═ p₀,p₁,...,p_M) And a component filter p_m＝(a_m,b_m,l_m)；

Firstly, on an SAR image training set, determining an initial value F of a root filter by a standard SVM method₀After interpolation processing is carried out on the root filter, a greedy algorithm is adopted to select a local area with the maximum positive weight square sum and the same size as the component filter on the double resolution as the initial value and the position of the mth component filter, and the position P is obtained_m＝(F_m,υ_m,s_m,d_m) In which F is_mRepresenting the component filter, v_mIs a two-dimensional vector representing the rectangular box offset position, s, of the mth component relative to the root filter_mIndicates the size of this rectangular box, d_mRepresenting a distortion cost vector, M ═ 1,2, …, M; clearing all weights of the region, and then continuously selecting the next component filter until all M component filters are initialized;

the root filter and the component filter are positioned in image sub-block X at z ═ p₀,p₁,...,p_M) As an implicit variable, where p_m＝(a_m,b_m,l_m) Characteristic pyramid ith of X_mIn the layer with the coordinates (a)_m,b_m) For the top left filter detection box, the corresponding feature vector is represented by phi (p)_m) Meaning that the fraction of the root filter is defined as F₀·φ(p₀) The fraction of the component filter is defined asWherein,measure the offset of part m, (a)₀,b₀) Representing the position coordinates of the root filter in the image pyramid, 2 (a)₀,b₀)+υ_mRepresenting the position coordinates of the component filter when the component filter is not deviated, and taking the position coordinates as an anchor point;

then, introducing an expansion factor based on the length-width ratio of the target, and expressing a total fraction calculation formula of the space position z as,

where g denotes the spreading factor, γ denotes the known target aspect ratio value, and the multi-component model parameter is expressed as β ═ F₀,F₁...,F_M,d₁,...,d_MG), the feature vectors corresponding to the multi-component model are represented as,

finally, the root filter and the component filters are updated by adopting a Latent SVM method, the process comprises the following two steps of iteration,

(a) keeping the beta value of the model parameter unchanged, searching the position with the highest score of each filter to obtain the optimal value of the hidden variable z, and then obtaining the feature vector of the optimal position;

(b) keeping the value of the implicit variable z of the sample unchanged, converting the parameter beta of the model into a segmentation hyperplane of the SVM, optimizing the beta through the following formula,

wherein f is_β(X) represents a penalty term, max (0, 1-yf)_β(X)) is a standard hinge loss function, C is a weight, y { -1,1} is a class label of X, -1 is a background, 1 is a target, Φ (X, z) is Φ (z)), the optimization of the β value is achieved by solving the convex programming problem defined in the above equation, by using a stochastic gradient descent method, for image block X, a gradient is calculated for the objective function of model parameters β,

wherein-y Φ (X, z (β)) is a gradient,approximated by-Ny Φ (X, z (β)), N representing the number of image sub-blocks, Φ (X, z (β)) representing Φ (z).

Compared with the prior art, the invention has the beneficial effects that:

the invention provides a novel SAR image target detection method based on mixed statistical distribution and a multi-component model by combining a mixed statistical distribution model and the multi-component model and introducing an expansion factor based on the length-width ratio of a target. And carrying out statistical modeling on the SAR image by adopting mixed distribution, combining the statistical modeling with the structural information, and developing the target detection result of the pixel level into the target detection result of the target level. On the basis, an expansion factor is introduced, and the model parameters are further adjusted and optimized by utilizing the target size information. The invention adds the characteristic of the target in the detection method, and can obtain better detection results.

Drawings

FIG. 1 is a flow chart of a mixed statistical distribution modeling of SAR images according to an embodiment of the present invention;

fig. 2 is a flowchart of model training and target detection of an SAR image according to an embodiment of the present invention.

Detailed Description

The technical scheme of the invention is explained in detail in the following by combining the drawings and the embodiment.

The invention provides a method for SAR image target detection based on mixed statistical distribution and a multi-component model by aiming at the statistical distribution characteristics of SAR images and combining target structure information and size information. And performing statistical modeling on a spatial pyramid of the SAR image by adopting mixed distribution, combining with a multi-component model, and developing a pixel-level target detection result into a target-level target detection result through a root filter and a component filter detection window. On the basis, an expansion factor is introduced, and the model parameters are further adjusted and optimized by utilizing the target size information.

The embodiment of the invention can adopt a computer software technology to realize automatic process operation, and comprises two stages, namely a mixed statistical distribution modeling stage and a model training and target detection stage.

Referring to fig. 1, the mixed statistical distribution modeling phase of an embodiment includes the following two steps:

step 1.1, respectively constructing a spatial pyramid for all SAR images in a training set, taking an original image as a bottom layer, and realizing the spatial pyramid in a sampling and smoothing way during specific implementation, which is not repeated in the invention; then, a mixed statistical distribution model is established for any layer of subimages in the pyramid, including that neighborhood subblocks X of all sample points of each layer of subimages in the pyramid are set to be { X }₁,...,x_nCarry out mixed statistical distribution modeling，x₁,…,x_nIndicating pixel points in the subblocks, wherein n indicates the number of the pixel points in the subblocks, and the number is determined by the size of a window taking a sample point as a center; its probability density function f (x) is expressed as a linear weighting of K statistical distributions:

wherein p is_i(θ_i) Representing the ith probability density distribution, θ, in the mixture distribution_iRepresenting a model parameter representing the ith probability density distribution, w_iA weight representing the ith probability density distribution,and w is not less than 0_iAnd K is less than or equal to 1, the number of the mixed statistical distribution models is represented by K, the value of K is determined according to the fitting degree, the fitting degree is better, and the value is larger.

The parameter vector to be estimated for each sample point is Θ ═ w₁,w₂,...,w_K；θ₁,θ₂,...,θ_K}. Therefore, the mixed distribution model of any layer of sub-images is represented as:

wherein N refers to the number of neighborhood sub-blocks, X_jRefers to the jth neighborhood sub-block.

Step 1.2, taking logarithm of expression of mixed statistical distribution model to obtain lnL (theta)

An Expectation Maximization (EM) algorithm is combined with a MoLC parameter estimation method to estimate parameters of the mixed statistical model, and the method is realized as follows:

(a) step E, let t represent iteration times, posterior probability based on current parameterExpressed as:

wherein,andrespectively representing the ith probability density distribution and probability weight after t iterations,representing the corresponding distribution parameters. Then, the label y of the distribution obeyed by each sample point x is determined according to the posterior probability^t(x) The label of the object is denoted by 1 and the background by-1.

(b) And M, estimating by adopting MoLC parameters: for the ith probability density distribution, the weight can be obtained by an estimation method based on a histogram, and is expressed by the formula:

wherein,representing a set of sample points subject to the ith probability density distribution. h (x) represents a histogram, i.e. the weight calculation process is to solve for the magnitude of the histogram contribution of the histogram of each distribution to the overall sample.

Updating the distribution parameter θ according to the MoLC equation^t+1The estimation method of the MoLC equation is expressed as:

wherein,representing the logarithmic moment.

The parameter updating is realized by adopting an EM iteration mode, initializing a parameter theta based on the MoLC, and then taking a label value with the maximum posterior probability as the final class of the image in the iteration process, wherein 1 represents a target and-1 represents a background.

The above process is repeated until a convergence state is reached.

Referring to FIG. 1, each probability density distribution in the mixture distribution is denoted as p₁(θ₁)…p_K(θ_K) Distribution weight is denoted as w₁…w_KThe distribution parameter theta in the parameter estimation result is obtained in the above manner_i|_{i＝1,2,…,K}And distribution weight w_i|_{i＝1,2,…,K}。

Referring to fig. 2, the model training and target detection phase of the embodiment includes the following two steps:

and 2.1, combining the mixed statistical distribution with a multi-component model according to the parameter estimation result obtained in the step 1, firstly determining the initial value and the position of a root filter and the initial value and the position of a component filter on an SAR image training set by a standard SVM method, then obtaining the scores of the root filter and the component filter by introducing an expansion factor based on the target length-width ratio, and finally updating the root filter and the component filter by adopting a Latent SVM method.

Example based on the parameter estimation result θ obtained in step 1_i|_{i＝1,2,…,K}And w_i|_{i＝1,2,…,K}Combining the mixed statistical distribution with a multi-component model, and determining an initial value F of a root filter on an SAR image training set by a standard SVM method₀After interpolation processing is performed on the root filter, a greedy algorithm is used to select a local region with the maximum positive weight square sum and the same size as the component filter in double resolution (the specific implementation is the prior art, and the details of the present invention are not repeated), which is used as the initial value and the position of the M (M is 1,2, …, M) th component filter, that is, the position P_m＝(F_m,υ_m,s_m,d_m) In which F is_mRepresenting the component filter, v_mIs a two-dimensional vector representing the rectangular box offset position, s, of the mth component relative to the root filter_mIndicates the size of this rectangular box, d_mRepresenting a distortion cost vector. All weights for this region are cleared and then the selection of the next component filter continues until the initialization of all M component filters is completed.

Combining the mixed statistical distribution with the multi-component model, wherein distribution parameters obtained by the statistical distribution are used as the characteristic description of the target in the component model, and the corresponding parameters comprise mixed statistical distribution model parameters theta { w ═ w }₁,w₂,...,w_K；θ₁,θ₂,...,θ_KAnd component model position information parameter P_m＝(F_m,υ_m,s_m,d_m) Hidden variable z ═ p₀,p₁,...,p_M) And a component filter p_m＝(a_m,b_m,l_m)。

The root filter and the component filter are positioned in image sub-block X at z ═ p₀,p₁,...,p_M) As an implicit variable, where p_m＝(a_m,b_m,l_m) Characteristic pyramid ith of X_mIn the layer with the coordinates (a)_m,b_m) For the top left filter detection box, the corresponding feature vector is represented by phi (p)_m) Representing that M refers to the number of the component filters, and the value of M is 1 to M; the fraction of the root filter is thus defined as F₀·φ(p₀) The fraction of the component filter is defined as:wherein,measure the offset of part m, (a)₀,b₀) The position coordinates of the root filter in the image pyramid are represented, and the layer corresponding to the component filter is multiplied by 2. Thus, 2 (a)₀,b₀)+υ_mIndicating the position coordinates of the component filter when it is not shifted, i.e. the anchor point.

The locations of the root filter and the component filters, i.e., anchor points, may be obtained through a model training process. During the process of testing matching, the component filter will shift relative to the anchor point position, and the shift is the shiftThen further squaring can be performed

On the basis, an expansion factor based on the length-width ratio of the target is introduced, and the total fraction calculation formula of the space position z is expressed as follows:

the multi-component model parameter is expressed as β ═ F (F)₀,F₁...,F_M,d₁,...,d_MG), the feature vector corresponding to the multi-component model may be expressed as:

then, the root filter and the component filters are updated using the Latent SVM method. The process is mainly divided into the following two steps of iteration:

(a) keeping the value of the model parameter beta unchanged, searching the position with the highest score of each filter, namely the optimal value of the hidden variable z, and then obtaining the feature vector of the optimal position.

(b) Keeping the value of the implicit variable z of the sample unchanged, converting the parameters β of the model into a segmentation hyperplane of the SVM, and optimizing β to obtain an optimization result β through the following formula^*：

Wherein f is_β(X) represents a penalty term, max (0, 1-yf)_β(X)) is a standard hinge loss function, C is weight, y { -1,1} is a class label of X, -1 represents background, 1 represents target, phi (X, z) is phi (z), the optimization of β value is realized by solving the convex programming problem defined in the formula, the step is mainly realized by a random gradient descent method (the specific realization is the prior art, and the invention is not repeated), and for the image block X, the gradient is calculated for the target function of the model parameter β

Wherein-y Φ (X, z (β)) is a gradient,can be approximated by-Ny phi (X, z (β)), where N represents the number of image sub-blocks, phi (X, z (β)) i.e., (phi:)z)。

And 2.2, constructing a mixed statistical distribution characteristic pyramid for all images in the SAR image training set, searching on each layer of the characteristic pyramid in a rectangular sliding window mode, sequentially recording the coordinates and the scores of the positions of the optimal root filters, the part filter labels and the part filter coordinates, and keeping the root filter window and the part filter window as a target detection frame when the comprehensive scores in the detection window are larger than a detection threshold value.

In the embodiment, a mixed statistical distribution characteristic pyramid is constructed for all images in the SAR image training set, and the specific construction mode is the same as that in the step 1. And then, searching on each layer of the characteristic pyramid by adopting a rectangular sliding window mode. And calculating the score of the root filter in each root filter detection window, and then searching a position with the maximum difference value obtained by subtracting a penalty term deviating from the reference position from the fraction of the component filter on a pyramid layer with twice resolution of the root filter by taking the position of the component filter obtained by training as a reference point. And (3) sequentially recording the coordinates and the scores of the positions of the optimal root filters, the part filter labels and the part filter coordinates, and calculating the final total score according to the formula (11):

and when the comprehensive score in the detection window is larger than the detection threshold value, reserving the root filter window and the component filter window as a target detection frame.

In order to verify the technical effect of the invention, the detection results of the targets such as airplanes, power towers, buildings and the like can be verified according to the high-resolution SAR image target detection method based on mixed statistical distribution and a multi-component model provided by the invention. As shown in tables 1 and 2, it can be seen from tables 1 and 2 that, under the condition of the same number of targets, the detection number of the invention is large, the false alarm number is 0, the detection rate of the target is obviously higher than that of other methods, and the performance of the invention is better than that of other methods by integrating all indexes.

TABLE 1 Wuhan area electric power tower target detection results (9 targets)

TABLE 2 target detection results (13 targets) for an airplane at a certain base

The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (4)

1. A SAR image target detection method based on mixed statistical distribution and a multi-component model is characterized by comprising the following steps:

step 1, carrying out mixed statistical distribution modeling on an SAR image training set, wherein the mixed statistical distribution modeling comprises the following substeps;

step 1.1, respectively constructing a spatial pyramid for all SAR images in a training set, and then establishing a mixed statistical distribution model for any layer of subimages in the pyramid;

step 1.2, taking logarithm of an expression of the mixed statistical distribution model, and then combining an expectation maximization algorithm with a MoLC parameter estimation method to estimate parameters of the mixed statistical model;

step 2, training a multi-component model and detecting a target, wherein the multi-component model training and target detection method comprises the following substeps;

step 2.1, according to the parameter estimation result obtained in the step 1, combining the mixed statistical distribution with a multi-component model, firstly determining the initial value and the position of a root filter and the initial value and the position of a component filter on an SAR image training set by a standard SVM method, then obtaining the fractions of the root filter and the component filter by introducing an expansion factor based on the target length-width ratio, and finally updating the root filter and the component filter by adopting a Latent SVM method;

and 2.2, constructing a mixed statistical distribution characteristic pyramid for all images in the SAR image training set, searching on each layer of the characteristic pyramid in a rectangular sliding window mode, sequentially recording the coordinates and the scores of the positions of the optimal root filters, the part filter labels and the part filter coordinates, and keeping the root filter window and the part filter window as a target detection frame when the comprehensive scores in the detection window are larger than a detection threshold value.

2. The method for detecting the target of the SAR image based on the mixed statistical distribution and the multi-component model as claimed in claim 1, wherein: the implementation manner of establishing the mixed statistical distribution model for any layer of the sub-images of the pyramid in the step 1.1 is as follows,

let X be { X ═ X₁,...,x_nDenotes the neighborhood sub-block of any layer of sub-image sample points, x₁,…,x_nThe pixel points in the subblocks are referred to, n refers to the number of the pixel points in the subblocks, the probability density function F (X) of the neighborhood subblocks is expressed as the linear weighting of K statistical distributions,

$F\left(X\right)=\underset{i=1}{\overset{K}{\Σ}}{w}_i{p}_i\left({\mathrm{\θ}}_i\right)---\left(1\right)$

wherein p is_i(θ_i) Representing the ith probability density distribution, θ, in the mixture distribution_iRepresenting a model parameter representing the ith probability density distribution, w_iA weight representing the ith probability density distribution,and w is not less than 0_iLess than or equal to 1, and K represents the number of the mixed statistical distribution models;

the parameter vector to be estimated for each sample point is Θ ═ w₁,w₂,...,w_K；θ₁,θ₂,...,θ_KAnd the mixed distribution model of any layer of sub-images is expressed as,

$L\left(\mathrm{\Θ}\right)=\underset{j=1}{\overset{N}{\Π}}F\left(X_j\right)---\left(2\right)$

wherein N refers to the number of neighborhood sub-blocks, X_jRefers to the jth neighborhood sub-block.

3. The method for detecting the SAR image target based on the mixed statistical distribution and the multi-component model as claimed in claim 1 or 2, characterized in that: in step 1.2, the expectation-maximization algorithm is combined with the MoLC parameter estimation method, and the parameters of the mixed statistical model are estimated in the following manner,

(a) step E, let t represent iteration times, posterior probability based on current parameterAs indicated by the general representation of the,

${\mathrm{\λ}}_{ij}^t\left(X\right)=\frac{w_i^t{p}_i\left({\mathrm{\θ}}_i^t\right)}{\underset{i=1}{\overset{K}{\Σ}}{w}_i^t{p}_i\left({\mathrm{\θ}}_i^t\right)}---\left(3\right)$

wherein,andrespectively representing the ith probability density distribution and probability weight after t iterations,representing the corresponding distribution parameters;

(b) m, adopting MoLC parameter estimation, obtaining the weight of the ith probability density distribution by a histogram-based estimation method, expressing the weight as the formula,

$w_i^{t+1}=\frac{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right)}{{\mathrm{\Σ}}_{x}h\left(x\right)}---\left(4\right)$

wherein,representing a set of sample points, y, subject to an ith probability density distribution^t(x) { -1,1} represents the label of the sample point x after t iterations, 1 represents the target, -1 represents the background, h (x) represents the straight lineA block diagram;

updating the distribution parameter θ according to the MoLC equation^t+1The estimation method of the MoLC equation is expressed as,

$\left\{\begin{array}{c}{k}_{1i}^t=\frac{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right)\ln x}{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right)}\\ k_{2i}^t=\frac{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right){(\ln x-k_{1i}^t)}^2}{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right)}\\ k_{3i}^t=\frac{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right){(\ln x-k_{1i}^t)}^3}{{\mathrm{\Σ}}_{x\∈S_i^t}h\left(x\right)}\end{array}\right.---\left(1\right)$

wherein,representing a logarithmic moment;

the parameter updating is realized by adopting an EM iteration mode, initializing a parameter theta based on the MoLC, and then taking a label value when the posterior probability is maximum as the final class of the image in the iteration process;

the above process is repeated until a convergence state is reached.

4. The SAR image target detection method based on the mixed statistical distribution and the multi-component model as claimed in claim 3, characterized in that: the implementation of said step 2.1 is as follows,

combining the mixed statistical distribution with the multi-component model, wherein distribution parameters obtained by the statistical distribution are used as the characteristic description of the target in the component model, and the corresponding parameters comprise mixed statistical distribution model parameters theta { w ═ w }₁,w₂,...,w_K；θ₁,θ₂,...,θ_KAnd component model position information parameter P_m＝(F_m,υ_m,s_m,d_m) Hidden variable z ═ p₀,p₁,...,p_M) And a component filter p_m＝(a_m,b_m,l_m)；

Firstly, on an SAR image training set, determining an initial value F of a root filter by a standard SVM method₀After interpolation processing is carried out on the root filter, a greedy algorithm is adopted to select the filter with the maximum positive weight with the same size as the component filter on the double resolutionThe local area of the quadratic sum is used as the initial value and position of the mth component filter to obtain the position P_m＝(F_m,υ_m,s_m,d_m) In which F is_mRepresenting the component filter, v_mIs a two-dimensional vector representing the rectangular box offset position, s, of the mth component relative to the root filter_mIndicates the size of this rectangular box, d_mRepresenting a distortion cost vector, M ═ 1,2, …, M; clearing all weights of the region, and then continuously selecting the next component filter until all M component filters are initialized;

the root filter and the component filter are positioned in image sub-block X at z ═ p₀,p₁,...,p_M) As an implicit variable, where p_m＝(a_m,b_m,l_m) Characteristic pyramid ith of X_mIn the layer with the coordinates (a)_m,b_m) For the top left filter detection box, the corresponding feature vector is represented by phi (p)_m) Meaning that the fraction of the root filter is defined as F₀·φ(p₀) The fraction of the component filter is defined asWherein,measure the offset of part m, (a)₀,b₀) Representing the position coordinates of the root filter in the image pyramid, 2 (a)₀,b₀)+υ_mRepresenting the position coordinates of the component filter when the component filter is not deviated, and taking the position coordinates as an anchor point;

then, introducing an expansion factor based on the length-width ratio of the target, and expressing a total fraction calculation formula of the space position z as,

$score\left(z\right)=\underset{m=0}{\overset{M}{\Σ}}{F}_m\·\mathrm{\φ}\left(p_m\right)-\underset{m=0}{\overset{M}{\Σ}}{d}_m\·\left({\tilde{a}}_m,{\tilde{b}}_m,{\tilde{a}}_m^2,{\tilde{b}}_m^2\right)+g\mathrm{\γ}---\left(6\right)$

where g denotes the spreading factor, γ denotes the known target aspect ratio value, and the multi-component model parameter is expressed as β ═ F₀,F₁...,F_M,d₁,...,d_MG), the feature vectors corresponding to the multi-component model are represented as,

$\mathrm{\Φ}\left(z\right)=\[\mathrm{\φ}\left(p_0\right),\mathrm{\φ}\left(p_1\right),\mathrm{...},\mathrm{\φ}\left(p_M\right),-{\tilde{a}}_1,-{\tilde{b}}_1,-{\tilde{a}}_1^2,-{\tilde{b}}_1^2,\mathrm{...},-{\tilde{a}}_M,-{\tilde{b}}_M,-{\tilde{a}}_M^2,-{\tilde{b}}_M^2,\mathrm{\γ}\]---\left(7\right)$

finally, the root filter and the component filters are updated by adopting a Latent SVM method, the process comprises the following two steps of iteration,

(a) keeping the beta value of the model parameter unchanged, searching the position with the highest score of each filter to obtain the optimal value of the hidden variable z, and then obtaining the feature vector of the optimal position;

(b) keeping the value of the implicit variable z of the sample unchanged, converting the parameter beta of the model into a segmentation hyperplane of the SVM, optimizing the beta through the following formula,

$\left\{\begin{array}{c}{\mathrm{\β}}^{*}=\underset{\mathrm{\β}}{\mathrm{argmin}}\frac{1}{2}\left|\right|\mathrm{\β}|{|}^2+C\underset{X}{\Σ}max(0,1-{\mathrm{yf}}_{\mathrm{\β}}(X\left)\right)\\ f_{\mathrm{\β}}\left(X\right)=\underset{z}{\max }\mathrm{\β}\mathrm{\Φ}(X,z)\end{array}\right.---\left(8\right)$

wherein f is_β(X) represents a penalty term, max (0, 1-yf)_β(X)) is a standard hinge loss function, C is a weight, y { -1,1} is a class label of X, -1 is a background, 1 is a target, Φ (X, z) is Φ (z)), the optimization of the β value is achieved by solving the convex programming problem defined in the above equation, by using a stochastic gradient descent method, for image block X, a gradient is calculated for the objective function of model parameters β,

$\▿L_D\left(\mathrm{\β}\right)=\mathrm{\β}+C\underset{X}{\Σ}\[-y\mathrm{\Φ}(X,z(\mathrm{\β}\left)\right)\]---\left(9\right)$

wherein-y Φ (X, z (β)) is a gradient,with-N_yΦ (X, z (β)) is approximated, N represents the number of image subblocks, and Φ (X, z (β)) represents Φ (z).